Boundary element formulations for the numerical solution of two-dimensional diffusion problems with variable coefficients

This is the post-print version of the final paper published in Computers & Mathematics with Applications. The published article is available from the link below. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. Copyright @ 2012 Elsevier B.V.This paper presents new formulations of the radial integration boundary integral equation (RIBIE) and the radial integration boundary integro-differential equation (RIBIDE) methods for the numerical solution of two-dimensional diffusion problems with variable coefficients. The methods use either a specially constructed parametrix (Levi function) or the standard fundamental solution for the Laplace equation to reduce the boundary-value problem (BVP) to a boundary–domain integral equation (BDIE) or boundary–domain integro-differential equation (BDIDE). The radial integration method (RIM) is then employed to convert the domain integrals arising in both BDIE and BDIDE methods into equivalent boundary integrals. The resulting formulations lead to pure boundary integral and integro-differential equations with no domain integrals. Furthermore, a subdomain decomposition technique (SDBDIE) is proposed, which leads to a sparse system of linear equations, thus avoiding the need to calculate a large number of domain integrals. Numerical examples are presented for several simple problems, for which exact solutions are available, to demonstrate the efficiency of the proposed approaches

Black holes, gravitational waves and fundamental physics: A roadmap

The grand challenges of contemporary fundamental physics-dark matter, dark energy, vacuum energy, inflation and early universe cosmology, singularities and the hierarchy problem-all involve gravity as a key component. And of all gravitational phenomena, black holes stand out in their elegant simplicity, while harbouring some of the most remarkable predictions of General Relativity: event horizons, singularities and ergoregions. The hitherto invisible landscape of the gravitational Universe is being unveiled before our eyes: the historical direct detection of gravitational waves by the LIGO-Virgo collaboration marks the dawn of a new era of scientific exploration. Gravitational-wave astronomy will allow us to test models of black hole formation, growth and evolution, as well as models of gravitational-wave generation and propagation. It will provide evidence for event horizons and ergoregions, test the theory of General Relativity itself, and may reveal the existence of new fundamental fields. The synthesis of these results has the potential to radically reshape our understanding of the cosmos and of the laws of Nature. The purpose of this work is to present a concise, yet comprehensive overview of the state of the art in the relevant fields of research, summarize important open problems, and lay out a roadmap for future progress. This write-up is an initiative taken within the framework of the European Action on 'Black holes, Gravitational waves and Fundamental Physics'. © 2019 IOP Publishing Ltd

The enzymatic basis for pesticide bioremediation

Enzymes are central to the biology of many pesticides, influencing their modes of action, environmental fates and mechanisms of target species resistance. Since the introduction of synthetic xenobiotic pesticides, enzymes responsible for pesticide turnover have evolved rapidly, in both the target organisms and incidentally exposed biota. Such enzymes are a source of significant biotechnological potential and form the basis of several bioremediation strategies intended to reduce the environmental impacts of pesticide residues. This review describes examples of enzymes possessing the major activities employed in the bioremediation of pesticide residues, and some of the strategies by which they are employed. In addition, several examples of specific achievements in enzyme engineering are considered, highlighting the growing trend in tailoring enzymatic activity to a specific biotechnologically relevant function